|Speaker:||Tomoyuki Abe (University of Tokyo)|
|Title:||The theory of arithmetic D-modules and characteristic cycles|
|Date (JST):||Wed, Nov 17, 2010, 15:30 - 17:00|
In this talk, I want to introduce the characteristic cycles of arithmetic D-modules due to P. Berthelot, and talk about my recent results concerning this theory. The theory of D-modules was originated in Sato, Kashiwara, and others' research on integrable linear differential equation. A surprising thing is that "analysis" (which is "difficult" in some sense) can be interpreted by means of algebraic methods (namely cohomology theory, which is more or less easier).
I will discuss on the attempt to import this theory in the setting of "arrithmetic", and what we can do with this new tool.
After talking about the global picture of the theory, I will briefly review of the theory of Berthelot, and we will see the relation between characteristic cycles and Swan conductors.
Then I will introduce the ring of microdifferential operators for the further analysis on characteristic cycles.
We will conclude this talk by pointing out future applications of the theory, namely the theory of local Fourier transform, and conjectural stationary phase formula.